Typical Quantum Systems Research Articles

Experimental test of an extension of the Rosenzweig-Porter model to mixed integrable-chaotic systems experiencing time-reversal invariance violation

Abstract We report on the theoretical and experimental investigation of the transition of a typical quantum system with mixed regular-integrable classical dynamics to one with violated time-reversal (T) invariance. The measurements are performed with a flat superconducting microwave resonator with circular shape in which chaoticity is induced by using either long antennas or inserting two circular disks into the cavity, and by magnetizing a ferrite disk placed at its center, which leads to violation of T invariance. We propose an extension of the Rosenzweig-Porter (RP) model, which interpolates between mixed regular-chaotic instead of integrable dynamics and fully chaotic dynamics with violated T-invariance, and derive a Wigner-surmise like analytical expression for the corresponding nearest-neighbor spacing distribution. We propose a procedure involving this result and those for the RP model to determine the size of T-invariance violation and chaoticity and validate it employing the experimental eigenfrequency spectra.

Hamiltonian Identification via Quantum Ensemble Classification.

Identifying the Hamiltonian of an unknown quantum system is a critical task in the area of quantum information. In this article, we propose a systematic Hamiltonian identification approach via quantum ensemble multiclass classification (HI-QEMC). This approach is implemented by a three-step iterative refining process, i.e., parameter interval guess, verification, and judgment. In the parameter interval guess step, the parameter interval is divided into several sub-intervals and the true Hamiltonian parameter is guessed in one of them. In the parameter interval verification step, cross verification is applied to verify the accuracy of the guess. In the parameter interval judgment step, an adaptive interval judgment (AIJ) algorithm is designed to determine the sub-interval containing the true Hamiltonian parameter. Numerical results on two typical quantum systems, i.e., two-level quantum systems and three-level quantum systems, demonstrate the effectiveness and superior performance of the proposed approach for quantum Hamiltonian identification.

The Rosenzweig–Porter model revisited for the three Wigner–Dyson symmetry classes

Interest in the Rosenzweig–Porter model, a parameter-dependent random-matrix model which interpolates between Poisson and Wigner–Dyson (WD) statistics describing the fluctuation properties of the eigenstates of typical quantum systems with regular and chaotic classical dynamics, respectively, has come up again in recent years in the field of many-body quantum chaos. The reason is that the model exhibits parameter ranges in which the eigenvectors are Anderson-localized, non-ergodic (fractal) and ergodic extended, respectively. The central question is how these phases and their transitions can be distinguished through properties of the eigenvalues and eigenvectors. We present numerical results for all symmetry classes of Dyson’s threefold way. We analyzed the fluctuation properties in the eigenvalue spectra, and compared them with existing and new analytical results. Based on these results we propose characteristics of the short- and long-range correlations as measures to explore the transition from Poisson to WD statistics. Furthermore, we performed in-depth studies of the properties of the eigenvectors in terms of the fractal dimensions, the Kullback–Leibler (KL) divergences and the fidelity susceptibility. The ergodic and Anderson transitions take place at the same parameter values and a finite size scaling analysis of the KL divergences at the transitions yields the same critical exponents for all three WD classes, thus indicating superuniversality of these transitions.

Dissipation-Induced Photon Blockade in the Anti-Jaynes–Cummings Model

Due to the fundamental differences between the quantum world and the classical world, some phenomena, such as entanglement and wave–particle duality, only exist in the quantum realm. These peculiar phenomena cannot be demonstrated by classical means: Quantum networks, quantum cryptography, and quantum precision measurements all require quantum sources. Photons are particularly well-suited as quantum sources owing to their minimal interaction with the environment, high flight speed, and ease of interaction with current typical quantum systems. Single-photon sources include pulsed excitation of quantum dots, spontaneous parametric down-conversion, and photon blockade. Herein, we propose that the anti-Jaynes–Cummings model can induce a pronounced photon antibunching effect when subjected to intense cavity dissipation. Similar to the photon blockade caused by strong photon–photon interaction, this antibunching effect is referred to as ’dissipation-induced blockade’. Our findings indicate that the minimum decay rate of a qubit, coupled with a high decay rate for photons, is conducive to achieving strong antibunching within the system. Notably, g(2)(0)<g(2)(τ), a characteristic of photon antibunching, is only valid under the optimal condition Δ=0. Conversely, g(2)(0)<1 is satisfied across all parameters, indicating that g(2)(0)<1 is not a prerequisite for antibunching in the anti-Jaynes–Cummings model. Moreover, under the optimal conditions of the antibunching effect, the average photon number attains its peak value. Consequently, the current anti-Jaynes–Cummings model is promising for developing single-photon sources characterized by excellent purity and average photon number.

Properties of eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry

We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational (${C}_{3}$) symmetry. Its band structure exhibits two Dirac points (DPs) that are separated by a nearly flat band. We present a procedure that we employed to identify eigenfrequencies and to separate the eigenstates according to their transformation properties under rotation by $\frac{2\ensuremath{\pi}}{3}$ into the three ${C}_{3}$ subspaces. This allows us to verify previous numerical results of Zhang and Dietz [Phys. Rev. B 104, 064310 (2021)], thus confirming that the properties of the eigenmodes coincide with those of artificial graphene around the lower DP, and they are well described by a tight-binding model for a honeycomb-kagome lattice of corresponding shape. Above all, we investigate the properties of the wave-function components in terms of the fluctuation properties of the measured scattering matrix, which are numerically not accessible. They are compared to random-matrix theory predictions for quantum-chaotic scattering systems exhibiting extended or localized states in the interaction region, that is, the DB. Even in regions where the wave functions are localized, the spectral properties coincide with those of typical quantum systems with chaotic classical counterparts.

A model‐based systems engineering framework for quantum dot solar cells development

AbstractCurrently, a wide range of newly designed devices are based on high‐end quantum technologies. To successfully design a quantum system, it is necessary to appropriately address the increasing complexity which exists in the development procedure of the system. A suitable approach to deal with this problem is to employ systems engineering models and integrate them with domain engineering tools. The model‐based systems engineering (MBSE) methodology is commonly used to analyze, design, manufacture, and test various complex systems. In this paper, the MBSE approach is chosen for the development of quantum dot solar cells as a typical quantum system and to deal with the complexity existing in this procedure. The analysis, manufacturing, and verification, validation, and testing (VV&T) for this system are described using SysML in Cameo Systems Modeler software to represent the role of models in this regard. Then a detailed design is performed in MATLAB and integrated with SysML to identify how changing various parameters during the system development process affects the overall system performance. This technique facilitates the communication between different engineering teams and helps to manage the complexity in the entire system lifecycle.

Unidirectionality and Husimi functions in constant-width neutrino billiards

We investigate the spectral properties and Husimi functions of relativistic quantum billiards (QBs) consisting of a spin-1/2 particle governed by the Dirac equation and confined to a planar domain of constant-width (CW) by imposing boundary conditions (BCs) on the spinor components. We consider those of neutrino billiards (NBs) proposed in (Berry and Mondragon 1987 Proc. R. Soc. A 412 53). The classical dynamics of billiards of corresponding shape is predominantly chaotic. CW billiards attracted particular attention because they exhibit unusual properties. Their classical dynamics features unidirectionality, whereas in the corresponding nonrelativistic QB a change of the rotational direction of motion is possible via dynamical tunneling, and the spectral properties coincide with those of typical quantum systems with violated time-reversal invariance. Unidirectionality of the quantum dynamics would arise in the structure of the Husimi functions. We analyze them for two realizations of CW NBs in the ultra-relativistic, i.e. the massless case and for massive cases and come to the result, that the modes can be separated into clockwise and counterclockwise modes and dynamical tunneling is absent. This is attributed to the BCs and the unidrectionality of the local current arising from them.

Experimental study of closed and open microwave waveguide graphs with preserved and partially violated time-reversal invariance.

We report on experiments that were performed with microwave waveguide systems and demonstrate that in the frequency range of a single transversal mode they may serve as a model for closed and open quantum graphs. These consist of bonds that are connected at vertices. On the bonds, they are governed by the one-dimensional Schrödinger equationwith boundary conditions imposed at the vertices. The resulting transport properties through the vertices may be expressed in terms of a vertex scattering matrix. Quantum graphs with incommensurate bond lengths attracted interest within the field of quantum chaos because, depending on the characteristics of the vertex scattering matrix, its wave dynamic may exhibit features of a typical quantum system with chaotic counterpart. In distinction to microwave networks, which serve as an experimental model of quantum graphs with Neumann boundary conditions, the vertex scattering matrices associated with a waveguide system depend on the wave number and the wave functions can be determined experimentally. We analyze the spectral properties of microwave waveguide systems with preserved and partially violated time-reversal invariance, and the properties of the associated wave functions. Furthermore, we study properties of the scattering matrix describing the measurement process within the framework of random matrix theory for quantum chaotic scattering systems.

Local Measurement-Induced Minimal Decoherence and its variants

Based on quantum measurement, the existing quantum correlation (QC) measures are divided into two categories, one class based on minimal entropy-like difference of the measurement fore-and-aft system density matrix, and the other based on minimal trace-like geometric distance of the measurement fore-and-aft system density matrix. Here we provide another class of QC measure, Local Measurement-Induced Minimal Decoherence (LMIMD) which indicates the simple and clear relationship between QC and quantum coherence. Its physical picture is intuitive and clear. These also indicate that the design realization of its experiment detection and specific potential applications with the superiorities would be much easier. In terms of some typical quantum systems, we investigate and analyze the advantages and disadvantages of the LMIMD and its variants Local Eigen-Measurement-Induced Minimal Decoherence (LEMIMD) and Local Eigen-Measurement-Induced Decoherence (LEMID) compared with the existing two classes of QC measure.

Typical: A Theory of Typicality and Typicality Explanation

Typicality is routinely invoked in everyday contexts: bobcats are typically short-tailed; people are typically less than seven feet tall. Typicality is invoked in scientific contexts as well: typical gases expand; typical quantum systems exhibit probabilistic behaviour. And typicality facts like these support many explanations, both quotidian and scientific. But what is it for something to be typical? And how do typicality facts explain? In this paper, I propose a general theory of typicality. I analyse the notion of a typical property. I provide a formalism for typicality explanations, and I give an account of why typicality explanations are explanatory. Along the way, I show how typicality facts explain a variety of phenomena, from everyday phenomena to the statistical mechanical behaviour of gases. Finally, I argue that typicality is not the same thing as probability.

Exploring entropic uncertainty relation and dense coding capacity in a two-qubit X-state

The measurement precision for two incompatible observables in a typical quantum system can be improved by the aid of one particle as a quantum memory. In this work, we study the entropic uncertainty relation in the presence of quantum memory (EUR-QM) and dense coding capacity (DCC) for arbitrary two-qubit X-states, and then we obtain an explicit relationship between the lower bound of the uncertainty and DCC. As an example, we examine the thermal EUR-QM as well as DCC in two kinds of two-qubit spin squeezing models (one-axis twisting model and two-axis counter-twisting model) under an external magnetic field. In the following, we relate EUR-QM to DCC and show analytically that there is an anti-correlated relation between them, and especially in the ground state. Our results show that for both the models, the entropic uncertainty and its bound can be decreased by reinforcing the spin squeezing parameters or decreasing the temperature of the system. Notably, we reveal that the valid dense coding cannot carry out in the one-axis twisting model, nevertheless, if we properly choose the Hamiltonian parameters, the two-axis counter-twisting model not only carries out the valid dense coding but also the optimal dense coding surely can be achieved. Thereby, our observations might offer new insights into quantum measurement precision and the optimal dense coding for the regimes of various solid-state systems.

CO-EXISTENCE OF LOCALIZED MAGNETIC MOMENT AND DELOCALIZED ELECTRONIC SHELL IN SUB-NANOMETER KONDO-LIKE SYSTEMS

Looking for the smallest limit that the Kondo-like effect can be observed has been a long-standing interest in the field of fundamental physics. In this regard, we have investigated the interaction between a countable number of free electrons and a single impurity magnetic moment in two typical quantum systems Cu12Cr and Au19Cr clusters. Both icosahedral Cu12Cr and tetrahedral Au19Cr clusters tend to form a closed-shell electron structure. However, their magnetic moments are completely different. Using density functional theory calculations, we analyzed, discussed and proposed a co-existence picture of electronic and magnetic shell to explain the quenched and unquenched magnetic moment of Cu12Cr and Au19Cr. The finding results are expected to contribute to the understanding of molecular magnetism in bimetallic nanoclusters.

Numerical Methods for the Wigner Equation with Unbounded Potential

Unbounded potentials are always utilized to strictly confine quantum dynamics and generate bound or stationary states due to the existence of quantum tunneling. However, the existed accurate Wigner solvers are often designed for either localized potentials or those of the polynomial type. This paper attempts to solve the time-dependent Wigner equation in the presence of a general class of unbounded potentials by exploiting two equivalent forms of the pseudo-differential operator: integral form and series form (i.e., the Moyal expansion). The unbounded parts at infinities are approximated or modeled by polynomials and then a remaining localized potential dominates the central area. The fact that the Moyal expansion reduces to a finite series for polynomial potentials is fully utilized. Using a spectral collocation discretization which conserves both mass and energy, several typical quantum systems are simulated with a high accuracy and reliable estimation of macroscopically measurable quantities is thus obtained.

Quantum state conversion in opto-electro-mechanical systems via shortcut to adiabaticity

Adiabatic processes have found many important applications in modern physics, the distinct merit of which is that accurate control over process timing is not required. However, such processes are slow, which limits their application in quantum computation, due to the limited coherent times of typical quantum systems. Here, we propose a scheme to implement quantum state conversion in opto-electro-mechanical systems via a shortcut to adiabaticity, where the process can be greatly speeded up while precise timing control is still not necessary. In our scheme, by modifying only the coupling strength, we can achieve fast quantum state conversion with high fidelity, where the adiabatic condition does not need to be met. In addition, the population of the unwanted intermediate state can be further suppressed. Therefore, our protocol presents an important step towards practical state conversion between optical and microwave photons, and thus may find many important applications in hybrid quantum information processing.

Quantum mechanics from classical statistics

Quantum mechanics can emerge from classical statistics. A typical quantum system describes an isolated subsystem of a classical statistical ensemble with infinitely many classical states. The state of this subsystem can be characterized by only a few probabilistic observables. Their expectation values define a density matrix if they obey a "purity constraint". Then all the usual laws of quantum mechanics follow, including Heisenberg's uncertainty relation, entanglement and a violation of Bell's inequalities. No concepts beyond classical statistics are needed for quantum physics - the differences are only apparent and result from the particularities of those classical statistical systems which admit a quantum mechanical description. Born's rule for quantum mechanical probabilities follows from the probability concept for a classical statistical ensemble. In particular, we show how the non-commuting properties of quantum operators are associated to the use of conditional probabilities within the classical system, and how a unitary time evolution reflects the isolation of the subsystem. As an illustration, we discuss a classical statistical implementation of a quantum computer.

Supersymmetric Quantum Mechanics and SUSY Dependent SU(2) Symmetry for a Spin-1/2 Charged Particle in a Magnetic Field

We find that in a supersymmetric quantum mechanics (SUSY QM) system, in addition to supersymmetric algebra, an associated SU(2) algebra can be obtained by using semiunitary (SUT) operator and projection operator, and the relevant constants of motion can be constructed. Two typical quantum systems are investigated as examples to demonstrate the above finding. The first example is the quantum system of a nonrelativistic charged particle moving in x-y plane and coupled to a magnetic field along z-axis. The second example is provided with the Dirac particle in a magnetic field. Similarly there exists an SUτ (2) ⊗ SUσ (2) symmetry in the context of the relativistic Pauli Hamiltonian squared. We show that there exists also an SU(2) symmetry associated with the supersymmetry of the Dirac particle.

The improved quantization rule and the Langer modification

An improved quantization rule is used to obtain a generalized formulation of Langer modification. The relations between the improved quantization rule and the Langer modification are studied. Two typical quantum systems, hydrogen atom and harmonic oscillator, are studied to show the relations between them.

The Fejér average and the mean value of a quantity in a quasiclassical wave packet

The mean value of a quantity in an equally weighted wave packet was recently found in the classical limit to be the Fejér average of partial sums of Fourier series expansion of the classical quantity, and the number of stationary states in it is equal to that of partial sums. The incompleteness of the Fejér average in representing a classical quantity enables us to define a classical uncertainty relation which turns out to be the counterpart of the quantum one. In this paper, two typical quantum systems, a harmonic oscillator and a particle in an infinite square well, are used to illustrate the above-mentioned points.

A Model of the Cloud Chamber in Generalized Coherent State Formalism

Particle trajectory in the Wilson cloud chamber is explained by means of the perturbation theory and generalized coherent states. The model consists of an incoming particle, molecules and detectors (the immediate environment of the molecules). The particle and the molecules are treated as typical quantum systems, while each detector has many harmonic oscillators whose state are totally de­ scribed by generalized coherent states. If a molecule is ionized through interaction with a particle, the ionized excited state is stable, that is, the molecule does not return to the ground The stability of excited states of the molecule is a result of properties of the generalized coherent states of the detector interacting with the molecule. § 1. Inh:oduction In a previous paper l ) we have presented two models for the quantum measuring process with the help of generalized coherent (GC) states, and shown that the detectors in these models have many desirable functions as measuring apparatus. These models also indicate that the GC state formalism can become a powerful method for a unified description of various measuring processes.· The GC state formalism is based on a group theoretical method developed by many authors.2) Many quantum theories have some measure of the number of dynamical variables N (or lin); for a wide class of these quantum theories the large-N limit is known to simplify the dynamics dramatically. In these theories the vacuum expectation of any product of reasonable operators satisfies the factorization relation, that is, the expec­ tation approaches the product of each expectation of the operators in the large-N limit. As a result, fluctuations of these operators become irrelevant when N is large. Also in some sense quantum theories with large N behave like classical theories with a phase space, the Poisson bracket, and classical Hamiltoni~n. Coherence group and GC states play an important role in this group theoretical method. The GC state approach to quantum measurement may provide a link between the microscopic and macroscopic descriptions of detectors. The essential features of the Wilson cloud chamber have already been explained in two ways using the perturbation theory. The two ways come from the arbitrari­ ness in the concept of observation, i.e., whether the molecules ·to be ionized are regarded as belonging to the observed system or the observing apparatus. These treatments of the cloud chamber are justified from Copenhagen's point of view. 3 )-5) The difference between the above two ways will disappear in GC state formalism, because the molecules can only be the observed system, not the observing apparatus. An observing apparatus must, in our formalism, have GC states generated by applying elements of a coherence group to a base state. In this article, we will apply the GC state formalism to the above cloud chamber. An incoming particle and molecules are typical quantum systems; the environment of

A Model of the Cloud Chamber in Generalized Coherent State Formalism

Particle trajectory in the Wilson cloud chamber is explained by means of the perturbation theory and generalized coherent states. The model consists of an incoming particle, molecules and detectors (the immediate environment of the molecules). The particle and the molecules are treated as typical quantum systems, while each detector has many harmonic oscillators whose state are totally described by generalized coherent states. If a molecule is ionized through interaction with a particle, the ionized excited state is stable, that is, the molecule does not return to the ground state. The stability of excited states of the molecule is a result of properties of the generalized coherent states of the detector interacting with the molecule.